PARAMETRIC EIGENSTRUCTURE ASSIGNMENT BY OUTPUT-FEEDBACK CONTROL - THE CASE OF MULTIPLE-EIGENVALUES

This paper deals with closed-loop eigenstructure assignment by output-feedback control in linear multivariable systems for the general case of multiple eigenvalues. The approach is algebraic and operates directly on the closed-loop characteristic equation using fundamental properties of determinants and their derivatives. A compact form for the controller gain matrix is derived and expressed in terms of a set of parameter vectors that specify the non-uniqueness of the solution of the eigenvalue-assignment problem. Some of these parameter vectors assume restricted forms while others are free. A computational scheme is given in which the free parameter vectors are determined in such a way as to assign the corresponding eigenvectors and generalized eigenvectors in a weighted least-square-error sense. An illustrative numerical example is included.